The values of f(x) and g(x) are shown for selected values of x in the table below. x f(x) g(x) 0 0 1 1 3 2 2 6 4 3 9 8 4 12 16 Of these two functions, one is exponential and the other is linear. Determine which of the functions is linear, and explain why this must be the case.

Answer:900

Step-by-step explanation:

720=.80x

720/.80=900

to check it

900*.20=720

Answer: ≈1.71

Step-by-step explanation:

[tex]\displaystyle\\(5^\frac{2}{3}) ^\frac{1}{2} =\\\\5^{\frac{2}{3}(\frac{1}{2})} =\\\\5^\frac{2(1)}{3(2)} =\\\\5^\frac{1}{3} =\\\\\sqrt[3]{5} }=\\\\\approx1.71[/tex]

The Domain of the Function is {-2, -1, 0,1 ,2, 3, 4, 5} and the Range of the Function is {4, 3, 2, 1, 0, -1}

What are Functions?

A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable).

Solution:

We neeed to find the Domain and Range of the Function

Domain refers to all the values of x = {-2, -1, 0,1 ,2, 3, 4, 5}

Range refers to all the values of y = {4, 3, 2, 1, 0, -1}

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The plane with an angle of depression of 70° is closer to the airport.

The distance between the plane and the airport is 15957 feet.

There are three commonly used trigonometric identities.

Sin x = 1/ cosec x

Cos x = 1/ sec x

Tan x = 1/ cot x or sin x / cos x

Cot x = cos x / sin x

We have,

Two planes are flying at an altitude of 15,000 feet.

The angle of depression from one plane to the airport is 70°.

This means,

The distance of the plane from the airport.

Sin 70 = 15,000 / Distance

Distance = 15,000/ sin 70 = 15,000 / 0.94 = 15957 feet _____(1)

The angle of depression from one plane to the airport is 60°.

The distance of the plane from the airport.

Sin 60 = 15,000 / Distance

Distance = 15,000/ sin 60 = 15,000 / 0.87 = 17241 feet _____(2)

Thus,

The plane with an angle of depression of 70° is closer to the airport.

The distance between the plane and the airport is 15957 feet.

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The missing value after solving is 280 seconds .

Given :

james rode his bike 7 yards in 3 seconds. set up the table with the information you know. yards seconds 7 3 you got it!

Seconds :

The second ( s or sec ) is the International System of Units ( SI ) unit of time measurement.

Table :

yards           seconds

7                     3

120                 x

we need to find x :

1 yard = 7/3 seconds

120 yards = 7 / 3 * 120 seconds

= 7 / 1 * 40 seconds

= 7 * 40 seconds

= 280 seconds.

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Answer:

slope = -9/7 or (negative fraction 9 over 7)

Step-by-step explanation:

what is the slope of the line that passes through (−2, 3) and (5, −6)?

slope = change in y / change in x

slope = (3 - (-6) / (-2 - 5)

slope = 9/-7

slope = -9/7

from your options:

negative fraction 9 over 7

The surface area of the pyramid is [tex]3060mm^{2}[/tex].

If “P” is the base perimeter, “l” is the slant height, and “B” is the base area, then the total surface area of the regular pyramid formula is given by [tex]\frac{1}{2} PI+B[/tex]  Square units.

Given that the base is a square, therefore the area of the base is 30×30mm= 900mm².

So, B=900.

The perimeter of the base is equal to 4×30mm=120mm.

So, P=120.

The slant height is equal to 36mm.

So, I=36.

Now we will substitute the values in the surface area formula of the pyramid.

The surface area of the pyramid is equal to

[tex]\frac{1}{2}*120*36+900=3060mm^{2}[/tex]

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fog(x) =4x²+44x+12,

f(x) is quadratic function  whose value is x²+6x -4 at x.

so , we have asked the value of f(x) at x=g(x) , which another function whose value is 2x-8 .

so, by the concept of composition of functions we have to put the value 2x-8 in place of x in the f(x) function to get fog(x).

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Answer:

7x

Step-by-step explanation:

Answer:

x is 1000

Step-by-step explanation:

hope this helps

Using the square formula, the value of (1+i)^4 is -4.

The square formula is the algebraic identity which is used to find the square or difference of the sum of two terms. The square of sum of the two terms and can be calculated by multiplying the binomial by itself. The general form of square formula to find the square of the sum of two terms is given by: (a + b)^2 = a^2 + 2ab + b^2 where a and b are variables.

The given expression can be rewritten as binomial with exponent:

((1 + i)^2)^2

Using the square formula to find the square of the sum of two terms to the (1 + i)^2. Hence,

(1 + i)^2 = 1 + 2i + i^2

As 'i' iota is the square root of negative 1, i^2 = -1

1 + 2i -1 = 2i

Therefore,

(2i)^2 = 4i^2 = 4*-1 = -4

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The pencil was reduced by 1/6 of its original length. Hence, the correct option is Option C.

To calculate the fraction, you must divide the remaining length (15 cm) by the original length (18 cm). In order to get a fraction, you have to divide it by their highest common factor, which in this case is 3.

= \frac{15}{18}

= \frac{5}{6}

This is the length of the pencil left at the end of the day. To find the fraction used, you have to subtract this fraction from its whole.

= 1 - \frac{5}{6}

= \frac{5}{6} - \frac{5}{6}

= \frac{6-5}{6}

= \frac{1}{6}

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Therefore ,The marked point will now have the updated coordinates P' (2, 7).

When a figure is transferred from one area to another without altering its size, shape, or orientation, a translation takes place. If we know which way and how far the figure to be moved, we can draw the translation in the coordinate plane.

Here,

On an X-Y coordinate plane, a figure is plotted.

When translating a figure 7 units to the down, we must provide the coordinates of the indicated point in the original figure

"(x, y)" = "(x + m, y + n)"

In response to the query, we have

The specified point's coordinates are: P (5,4).

The new coordinates of the indicated spot after this figure is translated 6 units to the right will be -

P'( 5,4- 7) = P'(5, -3) (5, -3)

As a result, the designated point's new coordinates are P' (5, -3)

The new coordinates of the marked point will be - P'(5, -3)

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The equivalent of the expressions are as follows;

Two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Two expressions are equivalent if:

Hence, let's simplify the expression to find it equivalent.

Therefore,

3(3t - 4) - (2t + 10)

open the bracket

9t - 12 - 2t - 10

7t - 22

5(2t + 1) + (-7t + 28)

10t + 5 - 7t + 28

3t + 33

[tex](4t -\frac{8}{5} ) - (3-\frac{4}{3}t ) = 4t+\frac{4}{3}t - \frac{8}{5}- 3 = \frac{12t+4t}{3} +\frac{-8-15}{5} = \frac{16}{3}t - \frac{23}{5}[/tex]

[tex](-\frac{9}{2}t+4 )+(\frac{7}{4}t+33 ) = -\frac{9}{2}t+ \frac{7}{4}t + 4 + 33 = \frac{-18t+7t}{4} + 37 = \frac{25}{4}t+ 37[/tex]

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Answer: x=1

Step-by-step explanation:

Assume that "log" is the base-10 logarithm

log (2x)+log (5)=1

log 10{10}(2x)+log (5)=1

Assume that "log" is the base-10 logarithm

\log 10{10}(2x)+\log (5)=1

\log 10{10}(2x)+\log10{10}(5)=1

Apply the logarithm product identity

\log 10{10}(2x)+\log 10{10}(5)=1

log 10{10}(2x x 5)}=1

Answer:x=-5

Step-by-step explanation:

x2+10=0

0-10=-10

x2=-10

-10/2=-5

x=-5

The distance of a = 1 / 2 pi, b = 1 pi, and c = 3 / 2 pi.

The complete movement of an object, regardless of direction, is referred to as distance. The amount of ground a thing travels from its starting point to its destination is also referred to as distance.

Given:

The time, t = π / 2 sec,

Calculate the distance by using the formula given below,

[tex]Distance = r\times time[/tex]

So, for distance, a = 1 × π / 2 =  π / 2

for distance, b = 1 × π =  π

for distance, c = 1 × 3 π / 2 =  3 π / 2

Therefore, the distance of a = 1 / 2 pi, b = 1 pi, and c = 3 / 2 pi.

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Answer:

The answer should be 5

Step-by-step explanation:

Hope it helps

Answer:

a b over c = c √ab

25 1/2 = 2√25 to the power of 1 → A number to the power of 1 is itself

√25

5

Step-by-step explanation:

Answer:

To prove the given identity, we can start by multiplying both sides of the equation by (cosθ - sinθ) to obtain:

(cosθ/1 - tanθ) (cosθ - sinθ) - sin^2θ/(cosθ - sinθ) = (cosθ + sinθ)(cosθ - sinθ)

Expanding both sides of the equation gives us:

cos^2θ - tanθcosθ - sin^2θ = -sin^2θ + cos^2θ

We can simplify this equation to:

-tanθcosθ = -sin^2θ + cos^2θ

We can simplify this further by using the identity cos^2θ + sin^2θ = 1:

-tanθcosθ = 1 - 2sin^2θ

We can rearrange this equation to solve for sin^2θ:

sin^2θ = (1 + tanθcosθ)/2

This is the desired result, so we have successfully proved the given identity.

I hope this helps! Let me know if you have any questions.

Step-by-step explanation:

SELF EXPLANATORY

The expressions have, the first expression has degree 5, end behavior to ± infinite terms , zeros are h = 0, -1/2 , -1/2, 11 , 11 and 2 multiplicity -1/2 and 11 and sketch is drawn in image 1. And second expression has degree 4, end behavior to + infinite terms , zeros are x = 0,0, 3,-3. , 2 multiplicity of 0 and sketch is drawn in image 2.

An expression that consists of variables, constants, and exponents that is combined using mathematical operations like addition, subtraction, multiplication, and division is referred to as a polynomial.

Given that the expression ;

T(h) = h (2h + 1)²(h - 11)² and D(x) = 3x⁴ - 27x²

Now for the first expression T(h) = h (2h + 1)²(h - 11)²

Simplifying, the expression;

T(h) = h (2h + 1)²(h - 11)²

Degree of the highest polynomial of above expression is 5.

To find end behavior, we will find the factors of expression;

T(h) = h (2h + 1)²(h - 11)²

Here, h = 0,  (2h + 1)² = 0 , (h - 11)²= 0

h= 0 , h = -1/2 , -1/2 and h = 11 , 11

Multiplicity of -1/2 is 2 and 11 is 2.

End behavior, given expression has 2 pair of repeated roots.

And  (2h + 1)² ≥ 0 , (h - 11)²≥ 0

So the expression behavior depends on the term h alone.

And also it is an even polynomial.

So the graph of expression varies to infinity term for both positive and negative.

Zeros of the polynomial are  h = 0, -1/2 , -1/2, 11 , 11.

Sketch 1,

Now for the second expression D(x) = 3x⁴ - 27x²

Simplifying, the expression;

D(x) = 3x⁴ - 27x²

Degree of the highest polynomial of above expression is 4.

To find end behavior, we will find the factors of expression;

D(x) =3x²(x+3)(x−3)

Here, x = 0,0, 3,-3.

Multiplicity of 0 is 2.

End behavior, it is an odd polynomial. So the graph of expression varies to positive infinity.

Sketch 2,

Therefore, the first expression has degree 5, end behavior to ± infinite terms , zeros are h = 0, -1/2 , -1/2, 11 , 11 and 2 multiplicity -1/2 and 11 and sketch is drawn in image 1. And second expression has degree 4, end behavior to + infinite terms , zeros are x = 0,0, 3,-3. , 2 multiplicity of 0 and sketch is drawn in image 2.

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Answer: 61.9%

Step-by-step explanation:

First, add 16 and 26 together to get the total of chicken = 42

Then take 26 divided by 42, then times 100% = 61.9%

Answer: 13,900

Step-by-step explanation:

To round numbers to the nearest hundred, you always look at the place one down which is the tens place. The tens place is 5.

The options for 856 to round to is either 800 or 900.

The rule is that 0-4 rounds down, 5-9 rounds up. Since the tens place is 5, it will round up to 900.

Therefore, the answer would be 13,900.

Answer: 9 weeks

Step-by-step explanation:

Let x be the number of weeks

So the equation will be

1497 - 83x < 750

Subtract 1497 on both sides

-83x < -747

x < 9

So the answer is 9 weeks

The statements that are true in the right triangle are

A right angled triangle is a triangle in which one of its angles is 90°.

Since the area model at the right shows a right triangle with side lengths a, b, and c such that a² + b² = c².

If the side lengths a increases by a small amount, but the lengths a increases by a small amount, but the lengths b and c do not change, we  need to show which of the following statements will be true.

Now, if the side a increases by a small amount Δa, we have that

a + Δa > a

Squarring both sides, we have that

(a + Δa)² > a²

Adding b² to both sides, we have that

(a + Δa)² + b² > a² + b²

(a + Δa)² + b² > c²  since  a² + b² = c²

So, a² + b² > c² where a is the new value of a = a + Δa

Also, since a is perpendicular to b, we have that angle m∠ACB = 90°. Increasing a by a small amount  Δa does not change a from being perpendicular to b, so we still have that m∠ACB = 90°.

So, the statements that are true in the right triangle are

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As per the given probability, the two action that the base station would takes are, 1) increasing the transmission power, and 2) reducing the transmission rate.

Probability:

In statistics, probability refers the likelihood that an event will occur and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes.

Given,

Here we need to find the two actions that a base station could take to ensure that the loss probability of a transmitted frame does not increase.

Here we have given that, a mobile node gets farther and farther away from a base station,

And the two actions that a base station could take to ensure that the loss probability of a transmitted frame does not increase will be solve by  increased transmission power and then reduce the rate.

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The value of area under the normal curve at a z-score of 0.33 with respect to the mean is 0.63 (2 dp).

It is a value that describes the deviation of a value from the standard deviation. Z-score is the number of standard deviations a given data point lies above or below mean.

To find the area under the normal curve at a specific value of z we look into the normal distribution table.

At 0.33 we can see that the value is 0.6293. This value is given from the center, which is the mean of the data.

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Answer: The slope is Negative

Step-by-step explanation:

The slope is rising over run

Let's pick 2 points (-3,0) (0,-2)

The slope is -2/3

Therefore the part of expression of 48 represent the price per scarfs .

A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation. It is possible to multiply, divide, add, or subtract in math. (Mathematical Operator, Number or Variable, Expression) is the structure of an expression.

Here,

In the given the expression 483, represents the number 0f scarves and 48 represents the price per scarf Buyers are charged shipping fee of $4.75 for each scarf order:

Therefore, from the given we can see the 48 represents the price per scarf.

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The line given by the point slope equation y - 8 = 1/2 (x - 4) represents the linear function f(x) = [tex]\frac{1}{2}[/tex] x + 6.

Linear functions are those functions whose graph drawn is a straight line. It consists of one dependent variable and one independent variable.

Linear functions are usually represented as f(x) = y = p + qx.

The given equation of the line in point slope form is,

y - 8 = 1/2 (x - 4)

⇒ y - 8 = (1/2 × x) - (1/2 × 4)

⇒ y - 8 = 1/2x - 2

⇒ y = 1/2x -2 + 8

⇒ y = 1/2x + 6

When x = 0, y = f(0) = (1/2 × 0) + 6 ⇒ f(0) = 6

Hence linear function f(x) = [tex]\frac{1}{2}[/tex] x + 6 represents the line given by the point slope equation y - 8 = 1/2 (x - 4).

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